Pricing Single Name Credit Derivatives

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Pricing Single Name Credit Derivatives"

Transcription

1 Pricing Single Name Credi Derivaives Vladimir Finkelsein 7h Annual CAP Workshop on Mahemaical Finance Columbia Universiy, New York December 1, 2

2 Ouline Realiies of he CDS marke Pricing Credi Defaul Swaps Generaing Clean Risky Discouning Curve Effec of Recovery Value Hedging CDS Pricing Defaul in Foreign Currency 1

3 Credi Derivaives Size of he Marke Noional ($ billion) 1,8 1,6 1,4 1,2 1, BBA esimaed BBA forecas Year Approximaely 4% of he marke noional come from Credi Defaul Swaps 2

4 Realiies of CDS Marke Sandardized ISDA Credi Derivaives Definiions (1999) provides indusry-wide sandards and ease of execuion Two-way Credi Defaul Swap marke in Invesmen Grade and Emerging Markes, nascen HY CDS marke High spread volailiy: from 4% up o 3% Risk managemen wih a lack of liquidiy: Shor end of he yield curve Vs. long end Gap risk Wide range of spreads: from 3 bp o he sky is he limi Defaul is no a heoreical possibiliy bu a fac of life (Russia, Ecuador, Laidlaw, ec) Reasonably deep cash marke wih a variey of bonds Traded volailiy in EM (mosly shor mauriies) Illiquid longer erm volailiy hrough opions on CDS and Asse Swaps Increase in acive risk managemen and more raional credi pricing Widespread opporuniies o exploi pricing anomalies 3

5 Benchmark Curves for a Given Name Defaul-free Discouning Curve (PV of $1 paid wih cerainy) D(, ) = E = exp r d rˆ τ τ exp τ dτ Clean Risky Discouning Curve [CRDC] (PV of $1 paid coningen on no defaul ill mauriy, oherwise zero) λ τ dτ Z (, ) = E exp ( r τ + λ τ ) dτ has a meaning of defaul probabiliy a ime over ime period Z (, ) = D(, ) Q(, ) Q(, ) = exp ˆ λ τ dτ Q(, ) where is survival probabiliy ill ime, and is usually inerpreed λˆτ as forward (no expeced! ) probabiliy of defaul per uni ime τ dτ 4

6 Credi Defaul Swap Goldman, Sachs & Co. A basic credi derivaives insrumen: ABC is long defaul proecion ABC par S D wih frequency condiional on survival of a reference name XYZ ABC 1 REC S par accr condiional on defaul of a reference name XYZ REC is a recovery value of a reference bond Reference bond: no guaranied cash flows cheapes-o-deliver cross-defaul (cross-acceleraion) Assume same recovery value REC for all CDS of he same senioriy on a given name 5

7 Pricing CDS For corporae and EM coupon bonds a defaul claim is (Principal + Accrued Ineres) Recovery value has very lile sensiiviy o a srucure of bond cash flows For his Face Value Claim, REC = R, and PV of CDS is given by PV CDS T τ τ = S T E + (1 e d E R ( r + λ ) dτ ( r + λ ) T dτ R = R, R = E( R) Assume, and no correlaion of R wih spreads and ineres raes As Eq (1) is linear in R, CRDC jus depends on expeced value R, no on disribuion of R Pu PV of CDS =, and boosrapping allows us o generae a clean risky discouning curve 6 ) λ e τ τ d (1)

8 Generaing CRDC E A erm srucure of par credi spreads T par is given by he marke To generae CRDC we need o price boh legs of a swap No Defaul (fee) leg T ( r ) dτ T Defaul leg S + λ τ T, pare ST, par Z (, ) τ e d = ( r + λ ) dτ T ( r + λ ) T τ τ τ τ dτ T ~ ( 1 R ) λe d = (1 R) E λe d = (1- R) λz (, ) If correlaion beween credi spreads and ineres raes is no zero, ~ λ ˆ τ λ τ S, d d 7

9 Correlaion Adjusmen 8 Goldman, Sachs & Co. Need o ake ino accoun correlaion beween spreads and ineres raes o calculae adjused forward defaul probabiliy λ λ + aλ Defaul-free rae r~ condiional Defaul Probabiliy and Rae Adjusmens Vs. Mauriy on no defaul also needs o be adjused as ~ r = rˆ a λ Vols=8%,Volr=2%,MRs=.5,MRr=.5,Corr=.3, =6% r=5% Rae Adj DefProb Adj ~ = ˆ dz(, ) d = E ( r + λ )exp For high spreads and high volailiies an adjusmen is no negligible For given par spreads forward defaul probabiliy decreases wih increasing volailiy, correlaion and level of ineres raes and par spreads and ~ s + ~ r = sˆ + rˆ + λ τ dτ ( rτ )

10 Recovery Value For he Face Value Claim he price of a generic coupon bond can be approximaed prey accuraely as ~ L n B (, N ) = C n Z (, n ) + Z (, N n N ~ + R 1 nln 1Z (, n) Z (, N ) n where 1 is forward defaul-free floaing rae for period n Bond price goes o recovery value in defaul For he same defaul risk and recovery value, high coupon bond should rade a higher credi spread han a low coupon bond There are no generic risky zero coupon bonds wih non zero recovery Using CRDC and given recovery value srucure one can creae any synheic insrumen ) 9

11 More on Recovery Value Oher ways o model recovery value: Recovery of he Risky Price (Duffie-Singelon) : Defaul claim is a raded price jus before he defaul even Recovery of he Riskless Price: Defaul claim is given by defaul-free PV of he bond cash flows a he momen of defaul For a zero coupon bond his defaul claim corresponds o he claim on a face value a mauriy Boh mehods operae wih risky zero coupon bonds wih embedded recovery values. One can use convenional bond mah for risky bonds Boh mehods are no applicable in he real markes 1

12 Effec of Recovery Value Assumpions on Relaive Value Implicaions for pricing off-marke deals, synheic insrumens, risk managemen Example: Relaive bond value Same name, senioriy and mauriy, differen coupons For Recovery of Face Value N For Recovery of Risky/Riskless Price B C B C B = ( C C n= 1 C B = ( C C (, Risky zero coupon bonds wih embedded recovery value are given by n C n N n= 1 ) D(, n n ) Q(, n ) Z R n ) n ) Z R (, ) = E exp τ λ τ τ (1 R ) ( r + (1 R ) ) d D (, ) Q (, ) [(1 R ) Q (, R ] Z R (, ) = D (, ) ) + for Risky Claim for Riskless Claim 11

13 Defaul Probabiliy and Recovery For a given par credi spread curve defaul probabiliies depend on recovery value definiion Defaul Probabiliy Curve for Various Claim Types Par Spreads = 6% Volailiy = 4% R =.4 5.% 45.% 4.% 35.% 3.% 25.% 2.% 15.% 1.% FV Claim Risky Claim Riskless Claim 5.%.% Mauriy (yrs)

14 Hedging CDS books Two ypes of exposures: credi spread risk, defaul risk Goldman, Sachs & Co. Using N hedging insrumens (bonds or CDS) on can hedge a CDS porfolio agains (N-1) predeermined facors for spread moves + defaul Differen Recovery Value definiions resul in differen hedging posiions Robusness of hedging depends on spread curve inerpolaion mehod Transacion cos may be significan: need o opimize hedging sraegy When hedging wih bonds, bond/cds basis risk can be an issue In EM cheapes-o-deliver opion is equivalen o firs-o-defaul feaure For HY CDS equiy opions/shares should be considered as possible hedging insrumen 13

15 Pricing Defaul in Foreign Currency Assume ha one needs o sell defaul proecion in foreign currency and hedge i by buying proecion in $. Q: A wha level o sell? If here is no inerdependence beween credi spreads and forward FX, implied defaul probabiliies should say he same in foreign currency Due o he correlaion beween defaul spread and each of FX, dollar ineres raes, and foreign ineres raes, he defaul probabiliy in a foreign currency will differ from ha in dollars Two sources for he adjusmen: - Devaluaion condiional on defaul - Day-o-day spread/fx/ir correlaion 14

16 Adjusmen for FX jump condiional on Defaul FX rae jumps by - % when defaul occurs (e.g. devaluaion) As probabiliy of defaul (and FX jump) is given by λ, under no defaul condiions he foreign currency (FC) should have an excessive reurn in erms of USD (DC) given by λ o compensae for a possible loss of value α Consider a FC clean risky zero coupon bond (R=) wih an excessive F no defaul reurn λ ha compensaes for a possible defaul The posiion value in DC = (Bond Price in FC) * (Price of FC in DC) F An excessive reurn of he posiion in DC is λ α + λ The posiion should have he same excessive reurn as any oher risky bond in DC which is given by λ To avoid arbirage he FC credi spread should be F λ = λ ( 1 α ) An adjusmen can be subsanial 15

17 Quano Spread Adjusmen In he no defaul sae, correlaion beween FX rae and ineres raes on one side and he credi spread on anoher resuls in a quano adjusmen o he credi spread curve used o price a synheic noe in FC Consider hedges for a shor in synheic risky noe in FC sell defaul proecion in DC long FC, shor DC If DC srenghens as spreads widen, in order o hedge he noe we would need o buy back some defaul proecion and sell he foreign currency ha depreciaed. Our P&L would suffer and we would need o pass his addiional expense o a couner pary in a form of a negaive credi spread adjusmen For high correlaion he adjusmen can be significan 16

18 Quano Adjusmen (con d) Adjusmen for a DC fla spread curve of 6 bp. Spread MR is imporan Effec of Mean Reversion on Log-Normal Spread Spr ead Adj us me n (bp ) Mean Reversion Year Spread adjusmen decreases wih increasing mean reversion and consan spo volailiy. =.2, S=6%, r$=5%, rf=2%, σs=8%, σ$=12.5%, β$=, σf=4%, βs=.5, σx=2%, ρ$s=, ρfs=.5, ρxs=.7. All curves are fla. 17

19 Quano Adjusmen (con d) Assumpions on spread disribuion are imporan Difference of Normal and Log-Normal Spread Adjusmens Adjusmen Difference (N-LN) (bp) Mean Reversion Year Difference beween normal and log-normal adjusmen decreases as mean reversion is increased for consan spo volailiy 18

20 Conclusions For single-name insrumens pricing is well undersood Recovery value definiion can have an significan effec on pricing and hedging Hedging CDS wih bonds: basis risk canno be ignored The disincion beween EM and FI credi derivaives gradually disappears Consisency of pricing and hedging mehods becomes more and more imporan 19

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years.

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years. Currency swaps Wha is a swap? A swap is a conrac beween wo couner-paries who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiy-index-linked

More information

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.

YTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment. . Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure

More information

Chapter 9 Bond Prices and Yield

Chapter 9 Bond Prices and Yield Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value

More information

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis

Credit Index Options: the no-armageddon pricing measure and the role of correlation after the subprime crisis Second Conference on The Mahemaics of Credi Risk, Princeon May 23-24, 2008 Credi Index Opions: he no-armageddon pricing measure and he role of correlaion afer he subprime crisis Damiano Brigo - Join work

More information

Equity Correlation Trading. Silverio Foresi and Adrien Vesval Goldman Sachs NYU, April 2006

Equity Correlation Trading. Silverio Foresi and Adrien Vesval Goldman Sachs NYU, April 2006 Equiy Correlaion Trading Silverio Foresi and Adrien Vesval Goldman Sachs NYU, April 2006 Ouline Equiy Correlaion: Definiions, Producs and Trade Srucures Raionale: Evidence and Models Opporuniies: an Hisorical

More information

Stochastic Calculus, Week 10. Definitions and Notation. Term-Structure Models & Interest Rate Derivatives

Stochastic Calculus, Week 10. Definitions and Notation. Term-Structure Models & Interest Rate Derivatives Sochasic Calculus, Week 10 Term-Srucure Models & Ineres Rae Derivaives Topics: 1. Definiions and noaion for he ineres rae marke 2. Term-srucure models 3. Ineres rae derivaives Definiions and Noaion Zero-coupon

More information

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao, Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics 27 January 2008 Absrac We exend a reduced form model for

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Chapter 5. Interest Rate Term Structure and Arbitrage-Free Valuation

Chapter 5. Interest Rate Term Structure and Arbitrage-Free Valuation Universié Paris-Dauphine M Gesion menion Finance Fixed Income Markes Marchés de aux d'inérê S. Aboura (Maîre de conférences Chaper 5. Ineres Rae Term Srucure and Arbirage-Free Valuaion Yield curve Spo

More information

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities

Dynamic Option Adjusted Spread and the Value of Mortgage Backed Securities Dynamic Opion Adjused Spread and he Value of Morgage Backed Securiies Mario Cerrao and Abdelmadjid Djennad Universiy of Glasgow Deparmen of Economics Previous Draf: 27 January 28 This Draf: 27 April 29

More information

Technical Description of S&P 500 Buy-Write Monthly Index Composition

Technical Description of S&P 500 Buy-Write Monthly Index Composition Technical Descripion of S&P 500 Buy-Wrie Monhly Index Composiion The S&P 500 Buy-Wrie Monhly (BWM) index is a oal reurn index based on wriing he nearby a-he-money S&P 500 call opion agains he S&P 500 index

More information

Risk Modelling of Collateralised Lending

Risk Modelling of Collateralised Lending Risk Modelling of Collaeralised Lending Dae: 4-11-2008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies

More information

Markit Excess Return Credit Indices Guide for price based indices

Markit Excess Return Credit Indices Guide for price based indices Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual

More information

CBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM )

CBOE VIX PREMIUM STRATEGY INDEX (VPD SM ) CAPPED VIX PREMIUM STRATEGY INDEX (VPN SM ) CBOE VIX PREIU STRATEGY INDEX (VPD S ) CAPPED VIX PREIU STRATEGY INDEX (VPN S ) The seady growh of CBOE s volailiy complex provides a unique opporuniy for invesors inen on capuring he volailiy premium.

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)

A Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM) A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke

More information

First Results and Implications for Hedge Accounting under IAS 39

First Results and Implications for Hedge Accounting under IAS 39 3.4 Firs Resuls and Implicaions for Hedge Accouning under IAS 39 3.4. Marke Segmenaion As discussed above marke segmenaion is characerisic for financial markes. In he following some examples concerning

More information

Collateral Posting and Choice of Collateral Currency

Collateral Posting and Choice of Collateral Currency Collaeral Posing and Choice of Collaeral Currency -Implicaions for derivaive pricing and risk managemen- Masaaki Fujii, Yasufumi Shimada, Akihiko Takahashi KIER-TMU Inernaional Workshop on Financial Engineering

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

A Note on Construction of Multiple Swap Curves with and without Collateral

A Note on Construction of Multiple Swap Curves with and without Collateral A Noe on Consrucion of Muliple Swap Curves wih and wihou Collaeral Masaaki Fujii, Yasufumi Shimada, Akihiko Takahashi Absrac There are now available wide variey

More information

Diagnostic Examination

Diagnostic Examination Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

Equities: Positions and Portfolio Returns

Equities: Positions and Portfolio Returns Foundaions of Finance: Equiies: osiions and orfolio Reurns rof. Alex Shapiro Lecure oes 4b Equiies: osiions and orfolio Reurns I. Readings and Suggesed racice roblems II. Sock Transacions Involving Credi

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

1. Explain why the theory of purchasing power parity is often referred to as the law of one price.

1. Explain why the theory of purchasing power parity is often referred to as the law of one price. Chaper Review Quesions. xplain why he heory of purchasing power pariy is ofen referred o as he law of one price. urchasing ower ariy () is referred o as he law of one price because he deerminaion of he

More information

Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012

Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012 Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing Time-Varying Equiy Risk Premium The Japanese Sock Marke 1980-2012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA

More information

MARCH 2010 ON THE RISK RETURN PROFILE OF LEVERAGE AND INVERSE ETFS

MARCH 2010 ON THE RISK RETURN PROFILE OF LEVERAGE AND INVERSE ETFS MARCH 00 ON THE RISK RETURN PROFIE OF EVERAGE AND INVERSE ETFS STOXX IMITED ON THE RISK RETURN PROFIE OF EVERAGED AND INVERSE ETFS /6 We derive a model for he performance and sharpe-raio of leveraged and

More information

strategy T R U LY P E R S O N A L I Z E D

strategy T R U LY P E R S O N A L I Z E D Fund Selec Premier sraegy T R U LY P E R S O N A L I Z E D Invesing for your presen and fuure financial needs can seem overwhelming. I shouldn be, and i doesn have o be. Implemening a well-conceived invesmen

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

Lecture III: Finish Discounted Value Formulation

Lecture III: Finish Discounted Value Formulation Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal

More information

An Introductory Note on Two Curve Discounting 1

An Introductory Note on Two Curve Discounting 1 An Inroducory Noe on Two Curve Discouning LCH.Clearne Ld (LCH.Clearne), which operaes he world s leading ineres rae swap (IRS) clearing service, SwapClear, is o begin using he overnigh index swap (OIS)

More information

Option Put-Call Parity Relations When the Underlying Security Pays Dividends

Option Put-Call Parity Relations When the Underlying Security Pays Dividends Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,

More information

A Further Examination of Insurance Pricing and Underwriting Cycles

A Further Examination of Insurance Pricing and Underwriting Cycles A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING?

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING? Chaper 10: THE BASICS OF CAPITAL BUDGETING Should we build his plan? Topic Overview Projec Types Capial Budgeing Decision Crieria Payback Period Discouned Payback Period Ne Presen Value () Inernal Rae

More information

Skewness and Kurtosis Adjusted Black-Scholes Model: A Note on Hedging Performance

Skewness and Kurtosis Adjusted Black-Scholes Model: A Note on Hedging Performance Finance Leers, 003, (5), 6- Skewness and Kurosis Adjused Black-Scholes Model: A Noe on Hedging Performance Sami Vähämaa * Universiy of Vaasa, Finland Absrac his aricle invesigaes he dela hedging performance

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Cannibalization and Product Life Cycle Management

Cannibalization and Product Life Cycle Management Middle-Eas Journal of Scienific Research 19 (8): 1080-1084, 2014 ISSN 1990-9233 IDOSI Publicaions, 2014 DOI: 10.5829/idosi.mejsr.2014.19.8.11868 Cannibalizaion and Produc Life Cycle Managemen Ali Farrukh

More information

Integrating Real and Financial Options in Demand-Side Electricity Contracts. Shmuel Oren University of California at Berkeley

Integrating Real and Financial Options in Demand-Side Electricity Contracts. Shmuel Oren University of California at Berkeley Inegraing Real and Financial Opions in Demand-Side Elecriciy Conracs Shmuel Oren Universiy o Caliornia a Berkeley Presened a he Workshop on Coordinaion in Deregulaed Elecriciy Markes Saariselka, Finland,

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

The yield curve, and spot and forward interest rates Moorad Choudhry

The yield curve, and spot and forward interest rates Moorad Choudhry he yield curve, and spo and forward ineres raes Moorad Choudhry In his primer we consider he zero-coupon or spo ineres rae and he forward rae. We also look a he yield curve. Invesors consider a bond yield

More information

Stochastic Optimal Control Problem for Life Insurance

Stochastic Optimal Control Problem for Life Insurance Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

The option pricing framework

The option pricing framework Chaper 2 The opion pricing framework The opion markes based on swap raes or he LIBOR have become he larges fixed income markes, and caps (floors) and swapions are he mos imporan derivaives wihin hese markes.

More information

With the FX basis risk the circumstances are more complicated. Starting point of the following analysis is the definition of the fixed-to-float

With the FX basis risk the circumstances are more complicated. Starting point of the following analysis is the definition of the fixed-to-float Wih he FX basis risk he circumsances are more complicaed. Saring poin of he following analysis is he definiion of he fixed-o-floa cross currency swap in Equaion 6. Le s analyze he changes in presen value

More information

The Allocation of Interest Rate Risk and the Financial Sector

The Allocation of Interest Rate Risk and the Financial Sector The Allocaion of Ineres Rae Risk and he Financial Secor Juliane Begenau Sanford Monika Piazzesi Sanford & NBER May 2012 Marin Schneider Sanford & NBER Absrac This paper sudies US banks exposure o ineres

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

Annuity Decisions with Systematic Longevity Risk

Annuity Decisions with Systematic Longevity Risk Annuiy Decisions wih Sysemaic Longeviy Risk Ralph Sevens This draf: November, 2009 ABSTRACT In his paper we invesigae he effec of sysemaic longeviy risk, i.e., he risk arising from uncerain fuure survival

More information

Stochastic Calculus and Option Pricing

Stochastic Calculus and Option Pricing Sochasic Calculus and Opion Pricing Leonid Kogan MIT, Sloan 15.450, Fall 2010 c Leonid Kogan ( MIT, Sloan ) Sochasic Calculus 15.450, Fall 2010 1 / 74 Ouline 1 Sochasic Inegral 2 Iô s Lemma 3 Black-Scholes

More information

INDEX RULE BOOK Leverage, Short, and Bear Indices

INDEX RULE BOOK Leverage, Short, and Bear Indices INDEX RULE BOOK Leverage, Shor, and Bear Indices Version 14-01 Effecive from 1 June 2014 indices.euronex.com Index 1. Index Summary 1 2. Governance and Disclaimer 6 2.1 Indices 6 2.2 Compiler 6 2.3 Cases

More information

THE PERFORMANCE OF OPTION PRICING MODELS ON HEDGING EXOTIC OPTIONS

THE PERFORMANCE OF OPTION PRICING MODELS ON HEDGING EXOTIC OPTIONS HE PERFORMANE OF OPION PRIING MODEL ON HEDGING EXOI OPION Firs Draf: May 5 003 his Version Oc. 30 003 ommens are welcome Absrac his paper examines he empirical performance of various opion pricing models

More information

The Interest Rate Risk of Mortgage Loan Portfolio of Banks

The Interest Rate Risk of Mortgage Loan Portfolio of Banks The Ineres Rae Risk of Morgage Loan Porfolio of Banks A Case Sudy of he Hong Kong Marke Jim Wong Hong Kong Moneary Auhoriy Paper presened a he Exper Forum on Advanced Techniques on Sress Tesing: Applicaions

More information

FUTURES AND OPTIONS. Professor Craig Pirrong Spring, 2007

FUTURES AND OPTIONS. Professor Craig Pirrong Spring, 2007 FUTURES AND OPTIONS Professor Craig Pirrong Spring, 2007 Basics of Forwards and Fuures A forward conrac is an agreemen beween a buyer and a seller o ransfer ownership of some asse or commodiy ( he underlying

More information

FORWARD AND FUTURES CONTRACTS

FORWARD AND FUTURES CONTRACTS Page1 C H A P T E R 2 FORWARD AND FUTURES CONTRACTS 2.1 INTRODUCTION The main purpose of forward and fuures conracs is he managemen of risk. The exposure o risk as a resul of ransacing in he spo marke

More information

MSCI Index Calculation Methodology

MSCI Index Calculation Methodology Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...

More information

I. Basic Concepts (Ch. 1-4)

I. Basic Concepts (Ch. 1-4) (Ch. 1-4) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing

More information

Variance Swap. by Fabrice Douglas Rouah

Variance Swap. by Fabrice Douglas Rouah Variance wap by Fabrice Douglas Rouah www.frouah.com www.volopa.com In his Noe we presen a deailed derivaion of he fair value of variance ha is used in pricing a variance swap. We describe he approach

More information

RiskMetrics TM Technical Document

RiskMetrics TM Technical Document .P.Morgan/Reuers RiskMerics TM Technical Documen Fourh Ediion, 1996 New York December 17, 1996.P. Morgan and Reuers have eamed up o enhance RiskMerics. Morgan will coninue o be responsible for enhancing

More information

The performance of popular stochastic volatility option pricing models during the Subprime crisis

The performance of popular stochastic volatility option pricing models during the Subprime crisis The performance of popular sochasic volailiy opion pricing models during he Subprime crisis Thibau Moyaer 1 Mikael Peijean 2 Absrac We assess he performance of he Heson (1993), Baes (1996), and Heson and

More information

MSCI Hedged Indices MSCI FX Hedge Indices MSCI Global Currency Indices

MSCI Hedged Indices MSCI FX Hedge Indices MSCI Global Currency Indices MSCI Hedged Indices MSCI FX Hedge Indices MSCI Global Currency Indices Conens Conens... 2 Inroducion... 4 Secion 1: Common Principles in he Calculaion of MSCI Hedged, MSCI FX Hedge and MSCI Global Currency

More information

LEASING VERSUSBUYING

LEASING VERSUSBUYING LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss

More information

Double Entry System of Accounting

Double Entry System of Accounting CHAPTER 2 Double Enry Sysem of Accouning Sysem of Accouning \ The following are he main sysem of accouning for recording he business ransacions: (a) Cash Sysem of Accouning. (b) Mercanile or Accrual Sysem

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity

2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity .6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This

More information

Level I Study Handbook Sample

Level I Study Handbook Sample Level I Sudy Handbook Sample The UpperMark Sudy Handbooks for Level I are comprised of 3 Volumes, each covering abou 10 Topics from he CAIA curriculum. This is a sample of one of he Topic chapers. You

More information

Foreign Exchange and Quantos

Foreign Exchange and Quantos IEOR E4707: Financial Engineering: Coninuous-Time Models Fall 2010 c 2010 by Marin Haugh Foreign Exchange and Quanos These noes consider foreign exchange markes and he pricing of derivaive securiies in

More information

Dynamic Hybrid Products in Life Insurance: Assessing the Policyholders Viewpoint

Dynamic Hybrid Products in Life Insurance: Assessing the Policyholders Viewpoint Dynamic Hybrid Producs in Life Insurance: Assessing he Policyholders Viewpoin Alexander Bohner, Paricia Born, Nadine Gazer Working Paper Deparmen of Insurance Economics and Risk Managemen Friedrich-Alexander-Universiy

More information

Short-Term Trading for a Wind Power Producer

Short-Term Trading for a Wind Power Producer Shor-Term Trading for a Wind Power Producer Juan M. Morales Anonio J. Conejo Juan Pérez Univ. Casilla La Mancha Spain Sepember 2009 1 Wha 1. Aim 2. Moivaion 3. Problem descripion 4. Mahemaical formulaion

More information

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

More information

Interest Rate Parity, Money Market Basis Swaps, and Cross-Currency Basis Swaps

Interest Rate Parity, Money Market Basis Swaps, and Cross-Currency Basis Swaps Fixed Income Liquid Markes Research June 23 Ineres Rae Pariy, Money Marke Basis Swaps, and Cross-Currency Basis Swaps Bruce uckman, Pedro Porfirio Because he classic ineres rae pariy condiion requires

More information

Currency Options (1): Concepts and Uses

Currency Options (1): Concepts and Uses Overview Chaper 8 Currency Overview Overview Pus and Calls Some Jargon: IV, I-A-OTM, TV Raional Exercising Using (European) Pu-Call Pariy Advanages Summary Are Opions oo Expensive? Overview Overview Pus

More information

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets?

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets? Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weak-form of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien

More information

Chapter 6 Interest Rates and Bond Valuation

Chapter 6 Interest Rates and Bond Valuation Chaper 6 Ineres Raes and Bond Valuaion Definiion and Descripion of Bonds Long-erm deb-loosely, bonds wih a mauriy of one year or more Shor-erm deb-less han a year o mauriy, also called unfunded deb Bond-sricly

More information

ABSTRACT KEYWORDS. Term structure, duration, uncertain cash flow, variable rates of return JEL codes: C33, E43 1. INTRODUCTION

ABSTRACT KEYWORDS. Term structure, duration, uncertain cash flow, variable rates of return JEL codes: C33, E43 1. INTRODUCTION THE VALUATION AND HEDGING OF VARIABLE RATE SAVINGS ACCOUNTS BY FRANK DE JONG 1 AND JACCO WIELHOUWER ABSTRACT Variable rae savings accouns have wo main feaures. The ineres rae paid on he accoun is variable

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

Distance to default. Credit derivatives provide synthetic protection against bond and loan ( ( )) ( ) Strap? l Cutting edge

Distance to default. Credit derivatives provide synthetic protection against bond and loan ( ( )) ( ) Strap? l Cutting edge Srap? l Cuing edge Disance o defaul Marco Avellaneda and Jingyi Zhu Credi derivaives provide synheic proecion agains bond and loan defauls. A simple example of a credi derivaive is he credi defaul swap,

More information

Structured products: Pricing, hedging and applications for life insurance companies

Structured products: Pricing, hedging and applications for life insurance companies U.U.D.M. Projec Repor 2009:4 Srucured producs: Pricing, hedging and applicaions for life insurance companies Mohamed Osman Abdelghafour Examensarbee i maemaik, 30 hp Handledare och examinaor: Johan Tysk

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Value at Risk part II. Weighted Historical Simulation. BRW Approach. HW Approach

Value at Risk part II. Weighted Historical Simulation. BRW Approach. HW Approach Value a Risk par II Weighed Hisorical Simulaion Chuang I - Yuan Deparmen of Finance, NCCU Weighed Hisorical Simulaion 3 BRW Approach 4 Boudoukh, Richardson and Whielaw (Risk, 998) Hull and Whie (JR, 998)

More information

Indexation of Principal Protection

Indexation of Principal Protection March 2008 Indexaion of Principal Proecion A S&P 500 Proecive Pu Index Concep Srikan Dash, CFA, FRM srikan_dash@sandp.com (212) 438 3012 Berlinda Liu berlinda_liu@sandp.com (212) 438 7834 Principal proeced

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

Introduction to Arbitrage Pricing

Introduction to Arbitrage Pricing Inroducion o Arbirage Pricing Marek Musiela 1 School of Mahemaics, Universiy of New Souh Wales, 252 Sydney, Ausralia Marek Rukowski 2 Insiue of Mahemaics, Poliechnika Warszawska, -661 Warszawa, Poland

More information

Developing Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion

Developing Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion Developing Equiy Release Markes: Risk Analysis for Reverse Morgage and Home Reversion Daniel Alai, Hua Chen, Daniel Cho, Kaja Hanewald, Michael Sherris Developing he Equiy Release Markes 8 h Inernaional

More information

Machine Learning in Pairs Trading Strategies

Machine Learning in Pairs Trading Strategies Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu

More information

Term Structure of Commodities Futures. Forecasting and Pricing.

Term Structure of Commodities Futures. Forecasting and Pricing. erm Srucure of Commodiies Fuures. Forecasing and Pricing. Marcos Escobar, Nicolás Hernández, Luis Seco RiskLab, Universiy of orono Absrac he developmen of risk managemen mehodologies for non-gaussian markes

More information

Puttable and Extendible Bonds: Developing Interest Rate Derivatives for Emerging Markets

Puttable and Extendible Bonds: Developing Interest Rate Derivatives for Emerging Markets WP/03/01 Puable and Exendible Bonds: Developing Ineres Rae Derivaives for Emerging Markes Salih N. Nefci and André O. Sanos 003 Inernaional Moneary Fund WP/03/01 IMF Working Paper IMF Insiue Puable and

More information

CRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis

CRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis CRISES AND THE FLEXIBLE PRICE MONETARY MODEL Saranis Kalyviis Currency Crises In fixed exchange rae regimes, counries rarely abandon he regime volunarily. In mos cases, raders (or speculaors) exchange

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED

More information

INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS

INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,

More information